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\frac{x+\sin x}{1+\cos x}dx=\frac{x}{2\cos^2(x/2)}dx+\tan\frac{x}{2}dx=x\sec^2\frac{x}{2}d\frac{x}{2}+\tan\frac{x}{2}dx=xd\tan\frac{x}{2}}+\tan\frac{x}{2}dx=d(x}+\tan\fr ...

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